Finite Group Databasebeta

← Group #72310304

Character table — Group #72310304

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11222222244444444444444888888888888888161616161616161616161616161616161616161632323232323232323232323232323232323232323232323232323232323232326464646464646464
order12222222222222222222222222222222224444222244444444444444444444444444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-11-11-11-11-111-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−iii−i−i11-1-1ii−i−i
χ101111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-11-11-11-11-111-1-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiiiii−i−iii−i−i-1-111−i−iii
χ111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-11-11-11-11-111-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii11-1-1−i−iii
χ121111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-11-11-11-11-111-1-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i−i−iii−i−iii-1-111ii−i−i
χ131111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-11-1-111-1-11-1-111iiii−i−i−i−i-1-111−i−iii1111-1-1-1-1iiii−i−i−i−iii−i−i−i−iii-1-111−i−iii
χ141111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-11-1-111-1-11-1-111iiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiiiii−i−i−i−iii11-1-1ii−i−i
χ151111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-11-1-111-1-11-1-111−i−i−i−iiiii-1-111ii−i−i1111-1-1-1-1−i−i−i−iiiii−i−iiiii−i−i-1-111ii−i−i
χ161111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-11-1-111-1-11-1-111−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i−i−iiiii−i−i11-1-1−i−iii
χ1711111111111-1-111-1-1-1-111-1-11-1-111-1-1-1-1-1-11111-1-11-1111-1-1-111iiii−i−i−i−i1-11-1−i−iiiii−i−iii−i−i11-1-111-1-1−i−iiiii−i−ii−ii−i1-11-1
χ1811111111111-1-111-1-1-1-111-1-11-1-111-1-1-1-1-1-11111-1-11-1111-1-1-111iiii−i−i−i−i1-11-1−i−iii−i−iii−i−iii-1-111-1-111−i−iiiii−i−i−ii−ii-11-11
χ1911111111111-1-111-1-1-1-111-1-11-1-111-1-1-1-1-1-11111-1-11-1111-1-1-111−i−i−i−iiiii1-11-1ii−i−iii−i−iii−i−i-1-111-1-111ii−i−i−i−iiii−ii−i-11-11
χ2011111111111-1-111-1-1-1-111-1-11-1-111-1-1-1-1-1-11111-1-11-1111-1-1-111−i−i−i−iiiii1-11-1ii−i−i−i−iii−i−iii11-1-111-1-1ii−i−i−i−iii−ii−ii1-11-1
χ2111111111111-1-111-1-1-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1111-1111-1-1iiii−i−i−i−i-11-11ii−i−iii−i−iii−i−i11-1-111-1-1−i−iii−i−iii−ii−ii-11-11
χ2211111111111-1-111-1-1-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1111-1111-1-1iiii−i−i−i−i-11-11ii−i−i−i−iii−i−iii-1-111-1-111−i−iii−i−iiii−ii−i1-11-1
χ2311111111111-1-111-1-1-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1111-1111-1-1−i−i−i−iiiii-11-11−i−iiiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i−ii−ii1-11-1
χ2411111111111-1-111-1-1-1-111-1-11-1-111-1-1-1-1-1-11111-1-1-1111-1111-1-1−i−i−i−iiiii-11-11−i−iii−i−iii−i−iii11-1-111-1-1ii−i−iii−i−ii−ii−i-11-11
χ2511111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-111-1-1-11111-111-1-1-1-1111111111-1-11-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i-1-1-1-11111i−i−ii−iii−i
χ2611111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-111-1-1-11111-111-1-1-1-1111111111-1-11-1-1-1-1−i−iiiii−i−iii−i−i−i−iii-1-1-1-11111−iii−ii−i−ii
χ2711111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-111-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111ii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-1i−i−iii−i−ii
χ2811111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-111-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-1−iii−i−iii−i
χ2911111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-111-1-1-11-1-11-1-1-1111111111111-111-11111ii−i−i−i−iii−i−iiiii−i−i-1-1-1-1-1-1-1-1−iii−ii−i−ii
χ3011111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-111-1-1-11-1-11-1-1-1111111111111-111-11111−i−iiiii−i−iii−i−i−i−iii-1-1-1-1-1-1-1-1i−i−ii−iii−i
χ3111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-111-1-1-11-1-11-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii11111111−iii−i−iii−i
χ3211111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-111-1-1-11-1-11-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i11111111i−i−iii−i−ii
χ33222222222222222222222222222222-2-2-2-2-2-2-2-2-2-200-2-200000022-2-222-2-20000000000000000000000002-22-2000000000000
χ34222222222222222222222222222222-2-2-2-2-2-2-2-2-2-200-2-2000000-2-222-2-222000000000000000000000000-22-22000000000000
χ352222222222222-2-2-2-222-2-2-2-2222-2-2-2-222-2-2-2-222-2200-220000002i2i−2i−2i−2i−2i2i2i0000000000000000000000002i−2i−2i2i000000000000
χ362222222222222-2-2-2-222-2-2-2-2222-2-2-2-222-2-2-2-222-2200-22000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000−2i2i2i−2i000000000000
χ3722222222222-2-222-2-2-2-222-2-22-2-222-2-22222-2-2-2-22200-2-20000002i2i−2i−2i−2i−2i2i2i000000000000000000000000−2i2i2i−2i000000000000
χ3822222222222-2-222-2-2-2-222-2-22-2-222-2-22222-2-2-2-22200-2-2000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000002i−2i−2i2i000000000000
χ3922222222222-2-2-2-222-2-2-2-2222-2-2-2-222-2-222-2-2222-200-2200000022-2-222-2-2000000000000000000000000-22-22000000000000
χ4022222222222-2-2-2-222-2-2-2-2222-2-2-2-222-2-222-2-2222-200-22000000-2-222-2-2220000000000000000000000002-22-2000000000000
χ41222222222-2-222222222-2-222-2-2-22-2-2-2222222-2-2-2-222-2222222200000000-2-2-2-2000000000000000000000000000000000000
χ42222222222-2-222222222-2-222-2-2-22-2-2-2222222-2-2-2-2-2-2-22-2-2-2-2-2-2000000002222000000000000000000000000000000000000
χ43222222222-2-222222222-2-222-2-2-22-2-2-2-2-2-2-2-2-22222002-20000000000000000002-22-2000000000000000000002-22-200000000
χ44222222222-2-222222222-2-222-2-2-22-2-2-2-2-2-2-2-2-22222002-2000000000000000000-22-2200000000000000000000-22-2200000000
χ45222222222-2-222-2-2-2-22222-2-2-2-2-2-222222-2-2-2-2-2-22-200220000000000000000002i−2i−2i2i000000000000000000002i−2i−2i2i00000000
χ46222222222-2-222-2-2-2-22222-2-2-2-2-2-222222-2-2-2-2-2-22-20022000000000000000000−2i2i2i−2i00000000000000000000−2i2i2i−2i00000000
χ47222222222-2-222-2-2-2-22222-2-2-2-2-2-2222-2-2222222-222-2-2-22-222-2-200000000-2-222000000000000000000000000000000000000
χ48222222222-2-222-2-2-2-22222-2-2-2-2-2-2222-2-2222222-22-22-2-2-22-2-2220000000022-2-2000000000000000000000000000000000000
χ49222222222-2-2-2-222-2-2-2-2-2-2-2-2-2222-2222222-2-222-2-2002-20000000000000000002i−2i−2i2i00000000000000000000−2i2i2i−2i00000000
χ50222222222-2-2-2-222-2-2-2-2-2-2-2-2-2222-2222222-2-222-2-2002-2000000000000000000−2i2i2i−2i000000000000000000002i−2i−2i2i00000000
χ51222222222-2-2-2-222-2-2-2-2-2-2-2-2-2222-222-2-2-2-222-2-2222-2-222-2-2-22200000000-22-22000000000000000000000000000000000000
χ52222222222-2-2-2-222-2-2-2-2-2-2-2-2-2222-222-2-2-2-222-2-222-22-22-2222-2-2000000002-22-2000000000000000000000000000000000000
χ53222222222-2-2-2-2-2-222-2-22222-222-22-2-222-2-222222-222-2-222-2-2-2-200000000-222-2000000000000000000000000000000000000
χ54222222222-2-2-2-2-2-222-2-22222-222-22-2-222-2-222222-2-2-2-2-2-2-22222000000002-2-22000000000000000000000000000000000000
χ55222222222-2-2-2-2-2-222-2-22222-222-22-2-2-2-222-2-2-2-2-2200220000000000000000002-22-200000000000000000000-22-2200000000
χ56222222222-2-2-2-2-2-222-2-22222-222-22-2-2-2-222-2-2-2-2-220022000000000000000000-22-22000000000000000000002-22-200000000
χ574444-4-44-4-40000004-400444-404-40-400000000000000000000000000000000000000000000002-22-22-22-20000000000000000
χ584444-4-44-4-40000004-400444-404-40-40000000000000000000000000000000000000000000000-22-22-22-220000000000000000
χ594444-4-44-4-40000004-400-4-44-40-440400000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ604444-4-44-4-40000004-400-4-44-40-44040000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ614444-4-44-4-4000000-440044-440-440-400000000000000000000000000000000000000000000002-2-222-2-220000000000000000
χ624444-4-44-4-4000000-440044-440-440-40000000000000000000000000000000000000000000000-222-2-222-20000000000000000
χ634444-4-44-4-4000000-4400-4-4-4404-40400000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ644444-4-44-4-4000000-4400-4-4-4404-4040000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ65444-44-4-44-40044444-4-4-400-44000-40000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ66444-44-4-44-40044444-4-4-400-44000-4000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ67444-44-4-44-40044-4-4-44-4-4004-400040000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ68444-44-4-44-40044-4-4-44-4-4004-40004000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ69444-44-4-44-400-4-444-4444004-4000-40000000000000000000000000000000000000002-2-222-2-22000000000000000000000000
χ70444-44-4-44-400-4-444-4444004-4000-4000000000000000000000000000000000000000-222-2-222-2000000000000000000000000
χ71444-44-4-44-400-4-4-4-44-44400-4400040000000000000000000000000000000000000002-2-22-222-2000000000000000000000000
χ72444-44-4-44-400-4-4-4-44-44400-440004000000000000000000000000000000000000000-222-22-2-22000000000000000000000000
χ73444-4-44-4-44440000440000-4-4-400004-4000000000000000000004i−4i004i−4i000000000000000000000000000000000000000000
χ74444-4-44-4-44440000440000-4-4-400004-400000000000000000000−4i4i00−4i4i000000000000000000000000000000000000000000
χ75444-4-44-4-44440000-4-4000044-40000-44000000000000000000004-400-44000000000000000000000000000000000000000000
χ76444-4-44-4-44440000-4-4000044-40000-4400000000000000000000-44004-4000000000000000000000000000000000000000000
χ77444-4-44-4-44-4-40000440000-4-440000-4400000000000000000000004i−4i004i−4i0000000000000000000000000000000000000000
χ78444-4-44-4-44-4-40000440000-4-440000-440000000000000000000000−4i4i00−4i4i0000000000000000000000000000000000000000
χ79444-4-44-4-44-4-40000-4-4000044400004-400000000000000000000004-400-440000000000000000000000000000000000000000
χ80444-4-44-4-44-4-40000-4-4000044400004-40000000000000000000000-44004-40000000000000000000000000000000000000000
χ8144-4-4-4-4444004-400004-400000000000004-44-4000004000-4004-4000000000000000000000000000000000000000000000000
χ8244-4-4-4-4444004-400004-400000000000004-44-400000-4000400-44000000000000000000000000000000000000000000000000
χ8344-4-4-4-4444004-400004-40000000000000-44-4400004000-404-400000000000000000000000000000000000000000000000000
χ8444-4-4-4-4444004-400004-40000000000000-44-440000-400040-4400000000000000000000000000000000000000000000000000
χ8544-4-4-4-444400-440000-4400000000000004-4-4400004000-40-4400000000000000000000000000000000000000000000000000
χ8644-4-4-4-444400-440000-4400000000000004-4-440000-4000404-400000000000000000000000000000000000000000000000000
χ8744-4-4-4-444400-440000-440000000000000-444-4000004000-400-44000000000000000000000000000000000000000000000000
χ8844-4-4-4-444400-440000-440000000000000-444-400000-40004004-4000000000000000000000000000000000000000000000000
χ8988-888-8-8-880000000000000000000008-8000000000000000000000000000000000000000000000000000000000000000000
χ9088-888-8-8-88000000000000000000000-88000000000000000000000000000000000000000000000000000000000000000000
χ9188-88-88-88-8008-80000-880000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9288-88-88-88-800-8800008-80000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8888-8-80000000000000000000000000008-8000000000000000000000000000000000000000000000000000000000000
χ9488-8-8888-8-8000000000000000000000000000-88000000000000000000000000000000000000000000000000000000000000
χ9516-1600000008-8008-800008-800000000000000000000000000000000000000000000000000000000000000000000000000000
χ9616-1600000008-800-880000-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ9716-160000000-88008-80000-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ9816-160000000-8800-8800008-800000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).